Problem: On the way to school, Karen became fixated on the puzzle game on her phone!

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The game is played as follows. In each level, you have a grid with n rows and m columns. Each cell originally contains the number 0.

One move consists of choosing one row or column, and adding 1 to all of the cells in that row or column.

To win the level, after all the moves, the number in the cell at the i-th row and j-th column should be equal to gi, j.

Karen is stuck on one level, and wants to know a way to beat this level using the minimum number of moves. Please, help her with this task!

Input

The first line of input contains two integers, n and m (1 ≤ n, m ≤ 100), the number of rows and the number of columns in the grid, respectively.

The next n lines each contain m integers. In particular, the j-th integer in the i-th of these rows contains gi, j (0 ≤ gi, j ≤ 500).

Output

If there is an error and it is actually not possible to beat the level, output a single integer -1.

Otherwise, on the first line, output a single integer k, the minimum number of moves necessary to beat the level.

The next k lines should each contain one of the following, describing the moves in the order they must be done:

  * row x, (1 ≤ x ≤ n) describing a move of the form "choose the x-th row". 
  * col x, (1 ≤ x ≤ m) describing a move of the form "choose the x-th column". 



If there are multiple optimal solutions, output any one of them.

Examples

Input

3 5
2 2 2 3 2
0 0 0 1 0
1 1 1 2 1


Output

4
row 1
row 1
col 4
row 3


Input

3 3
0 0 0
0 1 0
0 0 0


Output

-1


Input

3 3
1 1 1
1 1 1
1 1 1


Output

3
row 1
row 2
row 3

Note

In the first test case, Karen has a grid with 3 rows and 5 columns. She can perform the following 4 moves to beat the level:

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In the second test case, Karen has a grid with 3 rows and 3 columns. It is clear that it is impossible to beat the level; performing any move will create three 1s on the grid, but it is required to only have one 1 in the center.

In the third test case, Karen has a grid with 3 rows and 3 columns. She can perform the following 3 moves to beat the level:

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Note that this is not the only solution; another solution, among others, is col 1, col 2, col 3.

Solution (in PYTHON):

Solution:
from sys import stdin

rints = lambda: [int(x) for x in stdin.readline().split()]
rints_2d = lambda n: [rints() for _ in range(n)]
get_col = lambda arr, i: [row[i] for row in arr]

n, m = rints()
mat, ans, mat2 = rints_2d(n), [], []

for i in range(n):
    mi = min(mat[i])
    mat2.append([mi] * m)
    ans.extend(['row %d' % (i + 1)] * mi)

for j in range(m):
    diffs = set()
    for i in range(n):
        diffs.add(mat[i][j] - mat2[i][j])

    if len(diffs) != 1:
        ans = float('inf')
        break
    ans.extend(['col %d' % (j + 1)] * diffs.pop())

ans2, mat3 = [], [[0] * m for _ in range(n)]
for j in range(m):
    mi = min(get_col(mat, j))
    for i in range(n):
        mat3[i][j] = mi

    ans2.extend(['col %d' % (j + 1)] * mi)

for i in range(n):
    diffs = set([mat[i][j] - mat3[i][j] for j in range(m)])
    if len(diffs) != 1:
        ans2 = float('inf')
        break
    ans2.extend(['row %d' % (i + 1)] * diffs.pop())

if ans == ans2 == float('inf'):
    print(-1)
elif ans2 == float('inf'):
    print('%d\n%s' % (len(ans), '\n'.join(ans)))
elif ans == float('inf'):
    print('%d\n%s' % (len(ans2), '\n'.join(ans2)))
elif len(ans2) < len(ans):
    print('%d\n%s' % (len(ans2), '\n'.join(ans2)))
else:
    print('%d\n%s' % (len(ans), '\n'.join(ans)))